Why is this procedural displacement texture not showing up on render?
Don't use a mix shader node to mix RGB information.



The input for shaders and RGB information is quite different and cannot be mixed randomly. Read:

Cycles - (Shader) Nodes - inputs outputs - What are the exact data types?

and

Cycles - (Shader) Nodes - inputs outputs - What are the exact data types?

Real displacement is avaliable as an experimental feature only, So you need to enable "experimental" in the feature set and set the displacement to "true" or "both" in the materials section.



Read: Getting &quot;experimental&quot; true displacement to work

And the last, and most important piece, is that the plane needs some subdivisions for the displacement to work. A plane with just 4 vertices is not going to work for what you need, so in edit mode add a few subdivisions to the mesh.